tan x + sec x = 2 cos x
Multiply equation by cos x
1 + sin x = 2 cos2 x
1 + sin x = 2(1 - sin2 x)
2 sin2 x + sin x - 1 = 0
(2 sin x - 1)(1 + sin x) = 0
sin x = 1/2 ; sin x = -1
So, there can be three solutions: 30°, 150° and 270°.
The correct option is B.